The physical and chemical properties of bimetallic nanoparticles can be optimized by tuning the particle composition. In this study, we identified CO adsorption and dissociation energetics on five Pt-Mo nanoparticles at different concentrations, the lowest energy Pt-7, Pt6Mo, Pt5Mo2, Pt4MO3, and Mo-7 clusters. We have shown that the CO adsorption and dissociation energies and preferred CO adsorption sites are largely dependent on the composition of the nanoparticles. As the Mo concentration increases, the strength of the C-O internal bond in the adsorption complex decreases, as indicated by a decrease in the C-O stretching frequency. Also, more Mo sites in the nanoparticle become available for CO adsorption, and the preferred CO adsorption site switches from Pt to Mo. For these reasons, dissociation of CO is energetically favorable on Pt4MO3 and Mo-7. On both compositions, we have shown that the dissociation paths begin with CO adsorbed on a Mo site in a multifold configuration, in particular in a tilted configuration. These findings provide insight on the effects of the composition on the chemical and catalytical properties of Pt-Mo nanoparticles, thereby guiding future experiments on the synthesis of nanoparticles, especially those that may be suitable for various desired applications containing CO.